Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[2]
[[.,.],.]=>[1,2]=>[1,2]=>[2]
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>[3]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[2,1]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[3]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>[4]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>[3,1]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,1,3]=>[2,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[1,2,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[3,1]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,2,3]=>[1,3]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[1,2,1]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[2,2]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[2,2]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>[4]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[2,2]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[1,3]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[4]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[5]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,1,3,2,4]=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[2,2,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[4,1]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,2,1,3,4]=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,1,4,3]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,1,4]=>[1,2,2]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,1,4]=>[3,2]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[1,3,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[1,2,1,1]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[1,3,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[4,1]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,2,3,4]=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,2,4,3]=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,3,2,4]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[1,1,2,1]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,1]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,3,4]=>[2,3]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[2,2,1]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,3,4]=>[2,3]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[2,2,1]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,1,2,5,4]=>[3,2]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[2,1,2]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,2,2]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[3,2]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[3,2]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[5]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[3,2]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,1,3,5]=>[2,3]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[1,2,2]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[3,2]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,2,3,5]=>[1,4]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[1,2,2]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,3]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[2,3]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[5]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,4]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[5]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[3,2,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[5,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>[2,2,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>[4,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[2,3,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[2,2,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>[3,2,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[2,3,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[5,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>[2,1,2,1]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>[2,3,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>[1,2,3]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>[1,2,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>[3,3]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>[3,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>[1,3,2]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>[1,2,1,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>[2,2,2]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>[1,3,2]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>[4,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[1,4,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[1,3,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>[1,2,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[1,1,2,1,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[1,3,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>[2,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[1,2,2,1]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[3,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[1,4,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[1,2,2,1]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,3,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[1,4,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[5,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>[1,2,2,1]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>[1,4,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>[1,1,2,2]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>[1,3,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>[1,1,3,1]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,1,2,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,2,2,1]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,1,3,1]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,4,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>[2,4]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>[2,3,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>[2,2,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,2,1]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,3,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[2,4]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>[2,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>[2,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[2,1,2,1]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[2,3,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>[3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>[3,2,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>[2,1,3]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[1,2,3]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,2,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>[3,3]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[3,2,1]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[3,3]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[3,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>[4,2]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>[3,1,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>[2,2,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[1,2,1,2]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[3,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>[1,3,2]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,2,1,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[2,2,2]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,1,2,4,6,5]=>[4,2]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,2,2]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[4,2]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[4,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[6]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>[4,2]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,1,3,2,4,6]=>[3,3]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>[2,2,2]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>[4,2]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,2,1,3,4,6]=>[2,4]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,1,4,3,6]=>[2,2,2]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,1,4,6]=>[1,2,3]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,1,4,6]=>[3,3]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>[1,3,2]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[1,2,1,2]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[2,2,2]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[1,3,2]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[4,2]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,2,3,4,6]=>[1,5]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>[1,3,2]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>[1,2,3]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,1,2,2]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,2]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,3,4,6]=>[2,4]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,2,2]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,3,4,6]=>[2,4]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[2,2,2]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,1,2,5,4,6]=>[3,3]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,1,3]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,2,3]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[3,3]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[3,3]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[6]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[3,3]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,1,3,5,6]=>[2,4]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[1,2,3]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[3,3]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,2,3,5,6]=>[1,5]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,2,3]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,4]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[2,4]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[6]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,4]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,5]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[6]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,1,2,3,5,4,6]=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>[4,2,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>[6,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,1,2,4,3,5,6]=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,1,2,4,3,6,5]=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,1,2,5,4,3,6]=>[3,2,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,1,2,4,5,3,6]=>[5,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>[3,3,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>[3,2,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,1,2,4,6,5,3]=>[4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>[3,3,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>[6,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,1,3,2,4,5,6]=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,1,3,2,4,6,5]=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,1,3,2,5,4,6]=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,1,3,2,6,5,4]=>[3,1,2,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,1,3,2,5,6,4]=>[3,3,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,1,4,3,2,5,6]=>[2,2,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,1,4,3,2,6,5]=>[2,2,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,1,3,4,2,5,6]=>[4,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,1,3,4,2,6,5]=>[4,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,1,5,3,4,2,6]=>[2,3,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,1,5,4,3,2,6]=>[2,2,1,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,1,3,5,4,2,6]=>[3,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,1,4,3,5,2,6]=>[2,3,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,1,3,4,5,2,6]=>[5,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>[2,4,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>[2,3,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,1,6,4,3,5,2]=>[2,2,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>[2,1,2,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>[2,3,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,1,3,6,4,5,2]=>[3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,1,3,6,5,4,2]=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,1,4,3,6,5,2]=>[2,2,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,1,3,4,6,5,2]=>[4,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>[2,4,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>[2,2,2,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,1,3,5,4,6,2]=>[3,3,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>[2,4,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>[6,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,2,1,3,4,5,6]=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,2,1,3,4,6,5]=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,2,1,3,5,4,6]=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,2,1,3,6,5,4]=>[2,2,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,2,1,3,5,6,4]=>[2,4,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,2,1,4,3,5,6]=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,2,1,4,3,6,5]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,2,1,5,4,3,6]=>[2,1,2,2]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,2,1,4,5,3,6]=>[2,3,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,2,1,6,4,5,3]=>[2,1,3,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,2,1,6,5,4,3]=>[2,1,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,2,1,4,6,5,3]=>[2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,2,1,5,4,6,3]=>[2,1,3,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,1,4,5,6,3]=>[2,4,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,3,2,1,4,5,6]=>[1,2,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,3,2,1,4,6,5]=>[1,2,3,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,3,2,1,5,4,6]=>[1,2,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,3,2,1,6,5,4]=>[1,2,1,2,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,1,5,6,4]=>[1,2,3,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,2,3,1,4,5,6]=>[3,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,2,3,1,4,6,5]=>[3,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,2,3,1,5,4,6]=>[3,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,2,3,1,6,5,4]=>[3,1,2,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,1,5,6,4]=>[3,3,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,4,2,3,1,5,6]=>[1,3,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,2,3,1,6,5]=>[1,3,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,4,3,2,1,5,6]=>[1,2,1,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,3,2,1,6,5]=>[1,2,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,2,4,3,1,5,6]=>[2,2,3]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,2,4,3,1,6,5]=>[2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,3,2,4,1,5,6]=>[1,3,3]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,1,6,5]=>[1,3,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,2,3,4,1,5,6]=>[4,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,1,6,5]=>[4,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,2,3,4,1,6]=>[1,4,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,2,4,3,1,6]=>[1,3,1,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,2,4,1,6]=>[1,2,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,4,3,2,1,6]=>[1,1,2,1,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,3,4,2,1,6]=>[1,3,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,2,5,3,4,1,6]=>[2,3,2]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,2,5,4,3,1,6]=>[2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,3,2,5,4,1,6]=>[1,2,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,2,3,5,4,1,6]=>[3,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,2,3,5,1,6]=>[1,4,2]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,3,2,5,1,6]=>[1,2,2,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,2,4,3,5,1,6]=>[2,3,2]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,1,6]=>[1,4,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,1,6]=>[5,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>[1,5,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>[1,4,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,6,2,4,3,5,1]=>[1,3,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>[1,2,2,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>[1,4,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,6,3,2,4,5,1]=>[1,2,3,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,6,3,2,5,4,1]=>[1,2,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,6,4,3,2,5,1]=>[1,1,2,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,6,3,4,2,5,1]=>[1,3,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>[1,1,3,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[1,1,2,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[1,2,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[1,1,3,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[1,4,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,6,3,4,5,1]=>[2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,6,3,5,4,1]=>[2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,6,4,3,5,1]=>[2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[2,1,2,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[2,3,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,6,4,5,1]=>[1,2,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[1,2,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,6,4,5,1]=>[3,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[3,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,2,3,6,5,1]=>[1,3,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[1,2,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[1,3,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[4,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>[1,5,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>[1,3,2,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,5,3,2,4,6,1]=>[1,2,3,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[1,1,2,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[1,3,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,5,3,4,6,1]=>[2,4,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[2,2,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[1,2,3,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[3,3,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>[1,5,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[1,2,3,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[2,4,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[1,5,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[6,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,7,2,3,4,6,5]=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,7,2,3,5,4,6]=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,7,2,3,6,5,4]=>[1,3,2,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,7,2,3,5,6,4]=>[1,5,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,7,2,4,3,5,6]=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,7,2,4,3,6,5]=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,7,2,5,4,3,6]=>[1,2,2,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,7,2,4,5,3,6]=>[1,4,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,7,2,6,4,5,3]=>[1,2,3,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,7,2,6,5,4,3]=>[1,2,2,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,7,2,4,6,5,3]=>[1,3,2,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,7,2,5,4,6,3]=>[1,2,3,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,7,2,4,5,6,3]=>[1,5,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,7,3,2,4,5,6]=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,7,3,2,4,6,5]=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,7,3,2,5,4,6]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,7,3,2,6,5,4]=>[1,2,1,2,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,7,3,2,5,6,4]=>[1,2,3,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,7,4,3,2,5,6]=>[1,1,2,3]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,7,4,3,2,6,5]=>[1,1,2,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,7,3,4,2,5,6]=>[1,3,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,7,3,4,2,6,5]=>[1,3,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,7,5,3,4,2,6]=>[1,1,3,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,7,5,4,3,2,6]=>[1,1,2,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,7,3,5,4,2,6]=>[1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,7,4,3,5,2,6]=>[1,1,3,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,7,3,4,5,2,6]=>[1,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,6,3,4,5,2]=>[1,1,4,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,6,3,5,4,2]=>[1,1,3,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,6,4,3,5,2]=>[1,1,2,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[1,1,1,2,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[1,1,3,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,6,4,5,2]=>[1,2,3,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[1,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[1,1,2,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[1,3,2,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,5,3,4,6,2]=>[1,1,4,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[1,1,2,2,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[1,2,3,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[1,1,4,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,5,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,3,4,5,6]=>[2,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,7,3,4,6,5]=>[2,4,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,4,6]=>[2,3,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,5,4]=>[2,2,2,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,7,3,5,6,4]=>[2,4,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,7,4,3,5,6]=>[2,2,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,7,4,3,6,5]=>[2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,7,5,4,3,6]=>[2,1,2,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,7,4,5,3,6]=>[2,3,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,6,4,5,3]=>[2,1,3,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[2,1,2,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[2,1,3,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,4,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>[2,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,7,3,4,6,5]=>[2,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,4,6]=>[2,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,5,4]=>[2,2,2,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,7,3,5,6,4]=>[2,4,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,7,4,3,5,6]=>[2,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,7,4,3,6,5]=>[2,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,7,5,4,3,6]=>[2,1,2,2]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,7,4,5,3,6]=>[2,3,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,6,4,5,3]=>[2,1,3,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[2,1,2,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[2,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[2,1,3,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[2,4,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,1,2,7,4,5,6]=>[3,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>[3,3,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,1,2,7,5,4,6]=>[3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,1,2,7,6,5,4]=>[3,1,2,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,3,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,7,4,5,6]=>[2,1,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,7,4,6,5]=>[2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,7,5,4,6]=>[2,1,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[2,1,1,2,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,1,3,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>[1,2,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>[1,2,3,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,7,5,4,6]=>[1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[1,2,1,2,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,2,3,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,4,5,6]=>[3,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>[3,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,7,5,4,6]=>[3,2,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[3,1,2,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[3,3,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>[3,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>[3,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,7,5,4,6]=>[3,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[3,1,2,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[3,3,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,1,2,3,7,5,6]=>[4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,1,2,3,7,6,5]=>[4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,1,3,2,7,5,6]=>[3,1,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,6,5]=>[3,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[4,2,1,3,7,5,6]=>[2,2,3]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,2,1,3,7,6,5]=>[2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,3,2,1,7,5,6]=>[1,2,1,3]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[1,2,1,2,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,7,5,6]=>[3,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[3,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,2,3,7,5,6]=>[1,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,2,3,7,6,5]=>[1,3,2,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,7,5,6]=>[1,2,1,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,2,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,5,6]=>[2,2,3]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>[2,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[2,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,1,2,4,7,5,6]=>[4,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,1,2,4,7,6,5]=>[4,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,7,5,6]=>[2,2,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,2,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>[1,3,3]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,5,6]=>[4,3]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[4,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>[4,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[4,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,1,2,3,4,7,6]=>[5,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[5,1,2,4,3,7,6]=>[4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,1,3,2,4,7,6]=>[3,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,1,4,3,2,7,6]=>[2,2,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[5,1,3,4,2,7,6]=>[4,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[5,2,1,3,4,7,6]=>[2,3,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,2,1,4,3,7,6]=>[2,2,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[5,3,2,1,4,7,6]=>[1,2,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[5,2,3,1,4,7,6]=>[3,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>[1,3,1,2]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[1,2,1,1,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[2,2,1,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[1,3,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[4,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,2,3,4,7,6]=>[1,4,2]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>[1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,5,3,2,4,7,6]=>[1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[1,1,2,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,3,4,7,6]=>[2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,5,3,4,7,6]=>[2,3,2]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[2,2,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,1,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[3,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[3,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[4,1,2,3,5,7,6]=>[5,2]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>[3,2,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,2,1,3,5,7,6]=>[2,3,2]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,2,2,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[3,2,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,2,2,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,3,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[2,3,2]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[5,2]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,4,2]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[5,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[5,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[7]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>[5,2]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,1,2,4,3,5,7]=>[4,3]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>[3,2,2]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>[5,2]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,1,3,2,4,5,7]=>[3,4]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,1,3,2,5,4,7]=>[3,2,2]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,1,4,3,2,5,7]=>[2,2,3]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,1,3,4,2,5,7]=>[4,3]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>[2,3,2]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>[2,2,1,2]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,1,3,5,4,2,7]=>[3,2,2]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>[2,3,2]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>[5,2]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,2,1,3,4,5,7]=>[2,5]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,2,1,3,5,4,7]=>[2,3,2]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,2,1,4,3,5,7]=>[2,2,3]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,2,1,5,4,3,7]=>[2,1,2,2]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,1,4,5,3,7]=>[2,3,2]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,3,2,1,4,5,7]=>[1,2,4]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,1,5,4,7]=>[1,2,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,2,3,1,4,5,7]=>[3,4]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,1,5,4,7]=>[3,2,2]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,2,3,1,5,7]=>[1,3,3]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,3,2,1,5,7]=>[1,2,1,3]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,2,4,3,1,5,7]=>[2,2,3]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,1,5,7]=>[1,3,3]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,1,5,7]=>[4,3]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>[1,4,2]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>[1,3,1,2]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,5,3,2,4,1,7]=>[1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[1,1,2,1,2]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[1,3,1,2]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,2,5,3,4,1,7]=>[2,3,2]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[2,2,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[1,2,2,2]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[3,2,2]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>[1,4,2]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[1,2,2,2]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[2,3,2]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[1,4,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[5,2]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,6,2,3,4,5,7]=>[1,6]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,6,2,3,5,4,7]=>[1,4,2]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,6,2,4,3,5,7]=>[1,3,3]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,6,2,5,4,3,7]=>[1,2,2,2]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,6,2,4,5,3,7]=>[1,4,2]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,6,3,2,4,5,7]=>[1,2,4]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,6,3,2,5,4,7]=>[1,2,2,2]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,6,4,3,2,5,7]=>[1,1,2,3]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,6,3,4,2,5,7]=>[1,3,3]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,5,3,4,2,7]=>[1,1,3,2]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[1,1,2,1,2]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[1,2,2,2]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[1,1,3,2]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,4,2]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,6,3,4,5,7]=>[2,5]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>[2,3,2]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,6,4,3,5,7]=>[2,2,3]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[2,1,2,2]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,3,2]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,6,3,4,5,7]=>[2,5]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>[2,3,2]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,6,4,3,5,7]=>[2,2,3]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[2,1,2,2]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[2,3,2]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,1,2,6,4,5,7]=>[3,4]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,2,2]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,6,4,5,7]=>[2,1,4]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,1,2,2]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,6,4,5,7]=>[1,2,4]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,2,2,2]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,6,4,5,7]=>[3,4]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[3,2,2]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,5,7]=>[3,4]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[3,2,2]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[4,1,2,3,6,5,7]=>[4,3]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>[3,1,3]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,2,1,3,6,5,7]=>[2,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[1,2,1,3]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[3,1,3]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,3,3]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,2,1,3]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,2,3]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[2,2,3]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[4,3]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,2,3]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,3]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[4,3]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[4,3]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[7]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>[4,3]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,1,3,2,4,6,7]=>[3,4]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>[2,2,3]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>[4,3]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,2,1,3,4,6,7]=>[2,5]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,1,4,3,6,7]=>[2,2,3]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,1,4,6,7]=>[1,2,4]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,1,4,6,7]=>[3,4]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>[1,3,3]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[1,2,1,3]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[2,2,3]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[1,3,3]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[4,3]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,2,3,4,6,7]=>[1,6]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>[1,3,3]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,5,3,2,4,6,7]=>[1,2,4]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[1,1,2,3]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,3]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,3,4,6,7]=>[2,5]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,2,3]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,3,4,6,7]=>[2,5]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[2,2,3]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,4]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,1,4]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,2,4]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[3,4]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[3,4]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[7]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,1,3,5,6,7]=>[2,5]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,2,4]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,6]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,2,4]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,5]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[2,5]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[7]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,5]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,6]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[7]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>[8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,7,6]=>[7,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,1,2,3,4,7,6,5]=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,1,2,3,6,5,4,7]=>[4,2,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,1,2,3,7,5,6,4]=>[4,3,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,1,2,3,7,6,5,4]=>[4,2,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[8,1,2,3,5,7,6,4]=>[5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,1,2,3,6,5,7,4]=>[4,3,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,1,2,3,5,6,7,4]=>[7,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,1,2,4,3,6,5,7]=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,1,2,4,3,7,6,5]=>[4,1,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,1,2,6,4,5,3,7]=>[3,3,2]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[8,1,2,6,5,4,3,7]=>[3,2,1,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,1,2,4,6,5,3,7]=>[4,2,2]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[8,1,2,5,4,6,3,7]=>[3,3,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,1,2,4,5,6,3,7]=>[6,2]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[8,1,3,2,4,5,7,6]=>[3,4,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,1,3,2,4,7,6,5]=>[3,2,2,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,1,3,2,5,4,6,7]=>[3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,1,3,2,5,4,7,6]=>[3,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[8,1,3,2,6,5,4,7]=>[3,1,2,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,1,3,2,7,5,6,4]=>[3,1,3,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[8,1,3,2,7,6,5,4]=>[3,1,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,1,4,3,2,5,6,7]=>[2,2,4]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[8,1,4,3,2,5,7,6]=>[2,2,3,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[8,1,4,3,2,6,5,7]=>[2,2,2,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[8,1,4,3,2,7,6,5]=>[2,2,1,2,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,1,4,3,2,6,7,5]=>[2,2,3,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[8,1,3,4,2,7,6,5]=>[4,1,2,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,1,3,4,2,6,7,5]=>[4,3,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[8,1,5,3,4,2,7,6]=>[2,3,2,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[8,1,3,7,4,6,5,2]=>[3,3,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[8,1,3,5,4,7,6,2]=>[3,2,2,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,1,3,4,5,6,7,2]=>[7,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,2,1,3,4,5,6,7]=>[2,6]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,2,1,3,4,6,5,7]=>[2,4,2]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[8,2,1,3,6,5,4,7]=>[2,2,2,2]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[8,2,1,3,7,6,5,4]=>[2,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,2,1,4,3,6,5,7]=>[2,2,2,2]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[8,2,1,5,4,3,7,6]=>[2,1,2,2,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,3,2,1,4,5,6,7]=>[1,2,5]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[8,3,2,1,4,6,5,7]=>[1,2,3,2]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[8,3,2,1,6,5,4,7]=>[1,2,1,2,2]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[8,3,2,1,5,6,4,7]=>[1,2,3,2]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[8,3,2,1,7,6,5,4]=>[1,2,1,2,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,2,3,1,4,5,6,7]=>[3,5]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[8,2,3,1,5,4,7,6]=>[3,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[8,2,3,1,6,5,4,7]=>[3,1,2,2]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,2,3,1,5,6,4,7]=>[3,3,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[8,2,3,1,7,5,6,4]=>[3,1,3,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[8,2,3,1,7,6,5,4]=>[3,1,2,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,4,3,2,1,5,6,7]=>[1,2,1,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[8,4,3,2,1,5,7,6]=>[1,2,1,3,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[8,4,3,2,1,6,7,5]=>[1,2,1,3,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,2,3,4,1,5,6,7]=>[4,4]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[8,2,5,3,4,1,7,6]=>[2,3,2,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,6,5,4,3,2,1,7]=>[1,1,2,1,1,2]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,2,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[1,1,3,1,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[1,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[1,1,2,2,1,1]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>[1,1,2,2,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>[1,2,3,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[1,2,1,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[1,1,2,1,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[1,2,2,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,8,2,3,4,5,7,6]=>[1,6,1]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[1,8,2,3,4,6,5,7]=>[1,5,2]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[1,8,2,3,7,6,5,4]=>[1,3,2,1,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,8,2,4,3,5,6,7]=>[1,3,4]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[1,8,2,4,3,6,5,7]=>[1,3,2,2]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[1,8,3,2,4,5,6,7]=>[1,2,5]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,8,3,2,5,4,7,6]=>[1,2,2,2,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[1,8,3,2,7,6,5,4]=>[1,2,1,2,1,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[1,8,5,4,3,2,6,7]=>[1,1,2,1,3]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,4,5,3,7,8,6,2]=>[1,8,5,4,3,2,7,6]=>[1,1,2,1,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[1,8,3,5,4,2,7,6]=>[1,2,2,2,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[1,8,7,3,4,5,6,2]=>[1,1,5,1]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[1,8,7,4,3,5,6,2]=>[1,1,2,3,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[1,8,7,4,3,6,5,2]=>[1,1,2,2,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[1,8,7,5,4,3,6,2]=>[1,1,1,2,2,1]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[1,8,7,4,5,3,6,2]=>[1,1,3,2,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>[1,1,1,2,1,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>[1,1,1,3,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>[1,1,4,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>[1,1,2,3,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[1,1,5,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,3,4,5,6,7]=>[2,6]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,8,3,4,7,6,5]=>[2,3,2,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,8,3,4,6,7,5]=>[2,5,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,8,3,5,4,7,6]=>[2,3,2,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,8,3,7,5,6,4]=>[2,2,3,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,8,3,7,6,5,4]=>[2,2,2,1,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[2,1,8,4,3,6,5,7]=>[2,2,2,2]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[2,1,8,4,5,3,7,6]=>[2,3,2,1]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,1,2,1,1]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,3,1,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,7,5,6,3]=>[2,2,3,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,2,2,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,8,3,4,6,7,5]=>[2,5,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[1,2,8,3,7,6,5,4]=>[2,2,2,1,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[1,2,8,3,6,5,7,4]=>[2,2,3,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,8,4,3,5,6,7]=>[2,2,4]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[1,2,8,5,4,3,6,7]=>[2,1,2,3]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[1,2,8,4,5,3,7,6]=>[2,3,2,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[1,2,8,7,4,5,6,3]=>[2,1,4,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>[2,1,4,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[3,1,2,8,4,6,7,5]=>[3,4,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,1,2,8,7,5,6,4]=>[3,1,3,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[3,1,2,8,7,6,5,4]=>[3,1,2,1,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[3,2,1,8,5,4,7,6]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,7,5,6,4]=>[2,1,1,3,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[2,1,1,2,1,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>[2,1,1,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,1,4,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>[1,2,5]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[1,3,2,8,4,6,5,7]=>[1,2,3,2]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>[1,2,1,2,1,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[1,2,1,3,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,4,5,6,7]=>[3,5]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>[3,1,2,1,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>[3,2,2,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>[3,5]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,4,6,5,7]=>[3,3,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,7,5,6,4]=>[3,1,3,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[3,1,2,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[3,2,2,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[3,1,3,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[3,4,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,1,2,3,8,5,6,7]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,1,2,3,8,5,7,6]=>[4,3,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,1,2,3,8,6,5,7]=>[4,2,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,3,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[4,1,3,2,8,5,6,7]=>[3,1,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,1,3,2,8,5,7,6]=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[4,1,3,2,8,6,5,7]=>[3,1,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[3,1,1,2,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[3,1,3,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[4,2,1,3,8,5,6,7]=>[2,2,4]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[4,2,1,3,8,5,7,6]=>[2,2,3,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,2,1,3,8,6,5,7]=>[2,2,2,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[2,2,1,2,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,8,5,6,7]=>[1,2,1,4]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,8,5,7,6]=>[1,2,1,3,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,8,6,5,7]=>[1,2,1,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[1,2,1,1,2,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[1,2,1,3,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,8,5,6,7]=>[3,1,4]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,8,5,7,6]=>[3,1,3,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[3,1,1,2,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[3,1,3,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[1,3,4]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[1,3,1,2,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,8,5,6,7]=>[1,2,1,4]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,2,1,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,5,6,7]=>[2,2,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,5,7,6]=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,6,5,7]=>[2,2,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,2,1,2,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,2,3,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,5,6,7]=>[2,2,4]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[2,2,1,2,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,1,2,4,8,5,6,7]=>[4,4]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[4,1,2,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,8,5,6,7]=>[2,2,4]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[2,2,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,5,6,7]=>[1,3,4]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,5,6,7]=>[4,4]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[4,1,2,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,5,6,7]=>[4,4]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[4,1,2,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[4,3,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[5,1,3,2,4,8,6,7]=>[3,2,3]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[5,2,1,4,3,8,7,6]=>[2,2,1,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,4,2,3,1,8,6,7]=>[1,3,1,3]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>[1,3,1,2,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,8,6,7]=>[1,2,1,1,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[1,2,1,1,2,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[2,2,1,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[1,3,1,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[4,1,2,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[1,5,2,3,4,8,6,7]=>[1,4,3]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[1,5,2,4,3,8,6,7]=>[1,3,1,3]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,8,6,7]=>[2,2,1,3]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,8,6,7]=>[1,2,2,3]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,6,7]=>[3,2,3]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,1,2,3,5,8,6,7]=>[5,3]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[5,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,8,6,7]=>[1,2,2,3]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[1,2,2,2,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[1,4,2,3,5,8,6,7]=>[1,4,3]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,1,2,4,5,8,6,7]=>[5,3]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,2,1]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,8,6,7]=>[1,4,3]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>[5,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[5,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,1,2,3,4,5,8,7]=>[6,2]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[6,1,2,5,4,3,8,7]=>[3,2,1,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[6,1,2,4,5,3,8,7]=>[5,1,2]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[6,1,3,2,5,4,8,7]=>[3,2,1,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[6,1,5,3,4,2,8,7]=>[2,3,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[6,2,1,4,3,5,8,7]=>[2,2,2,2]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[3,2,6,5,4,1,8,7]=>[6,3,2,1,4,5,8,7]=>[1,2,3,2]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[6,4,3,2,1,5,8,7]=>[1,2,1,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[1,1,2,1,1,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[1,3,1,1,2]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[6,2,5,3,4,1,8,7]=>[2,3,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[1,2,2,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,3,4,5,8,7]=>[2,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,6,3,5,4,8,7]=>[2,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,6,4,3,5,8,7]=>[2,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,2,1,2]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,3,1,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,2,2,2]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[1,2,1,2,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[3,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,2,2,2]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,1,2,3,4,6,8,7]=>[6,2]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[1,2,1,2,2]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,2,2,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[6,2]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[1,2,3,2]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[6,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[6,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,1,2,3,4,5,6,8]=>[8]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,1,2,3,4,6,5,8]=>[6,2]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,1,2,3,6,5,4,8]=>[4,2,2]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[7,1,3,6,5,4,2,8]=>[3,2,1,2]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,2,1,3,4,5,6,8]=>[2,6]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,2,1,4,3,6,5,8]=>[2,2,2,2]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[7,2,1,6,5,4,3,8]=>[2,1,2,1,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[7,2,1,5,4,6,3,8]=>[2,1,3,2]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[7,4,3,2,1,5,6,8]=>[1,2,1,4]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[7,4,3,2,1,6,5,8]=>[1,2,1,2,2]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,5,2,4,3,1,6,8]=>[1,3,1,3]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[2,3,5,4,7,6,1,8]=>[7,2,3,5,4,1,6,8]=>[3,2,3]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[7,6,3,2,5,4,1,8]=>[1,2,2,1,2]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[1,1,2,1,1,2]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[1,2,2,1,2]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>[1,1,3,1,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[1,4,1,2]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>[3,2,1,2]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>[4,2,2]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[1,7,2,3,4,5,6,8]=>[1,7]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>[1,7,2,3,4,6,5,8]=>[1,5,2]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>[1,7,2,4,3,5,6,8]=>[1,3,4]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[1,7,2,4,5,6,3,8]=>[1,5,2]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,1,3,2]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[1,3,2,7,4,5,6,8]=>[1,2,5]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[1,3,2,7,4,6,5,8]=>[1,2,3,2]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,4,5,6,8]=>[3,5]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,4,6,5,8]=>[3,3,2]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,1,2,3,7,5,6,8]=>[4,4]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,2,2]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,7,5,6,8]=>[1,2,1,4]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[1,2,1,2,2]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,2,3,7,5,6,8]=>[1,3,4]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,2,1,2,2]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,2,2,2]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[1,2,1,1,3]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[2,2,1,3]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,4,3]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,3,1,3]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,1,2,3]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,2,2,3]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[3,2,3]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[5,3]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[1,2,2,3]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,3]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,4,3]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[5,3]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,1,2,3,4,5,7,8]=>[8]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,1,2,3,5,4,7,8]=>[5,3]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>[6,2,3,1,4,5,7,8]=>[3,5]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[6,4,3,2,1,5,7,8]=>[1,2,1,4]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[2,4,3,6,5,1,7,8]=>[6,2,4,3,1,5,7,8]=>[2,2,4]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>[3,2,3]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[1,6,2,3,4,5,7,8]=>[1,7]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[1,6,2,4,3,5,7,8]=>[1,3,4]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[1,2,6,3,5,4,7,8]=>[2,3,3]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[1,3,2,6,4,5,7,8]=>[1,2,5]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[1,2,3,6,4,5,7,8]=>[3,5]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,4]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[1,2,1,4]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[2,2,4]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[8]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,4]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,2,1,4]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[2,2,4]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,4]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,7]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,3,4]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,2,5]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[3,5]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[8]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,5]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,2,5]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,7]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[8]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,6]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,7]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[8]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,7,8]=>[9]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9]=>[10]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,6,7,9]=>[9]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[10]
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[1,6,7,5,8,4,9,3,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,1,1,1,2,1,1,1,1]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,2,1,1,1,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,2,2,2,2]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[7,2]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[8,2]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[9,2]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[6,2,1]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,7,8]=>[6,3]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[1,8]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,9]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[11]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,10]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,8,3,9,2,10,1]=>[10,9,8,5,4,7,6,3,2,1]=>[1,1,1,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,7,6,8,5,9,2,10,1]=>[10,9,4,3,8,7,6,5,2,1]=>[1,1,2,1,2,1,1,1]
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,9,2,10,1]=>[10,9,6,5,4,3,8,7,2,1]=>[1,1,1,2,1,2,1,1]
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,9,2,10,1]=>[10,9,4,3,6,5,8,7,2,1]=>[1,1,2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,7,6,8,5,9,4,10,1]=>[10,3,2,9,8,7,6,5,4,1]=>[1,2,1,1,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,9,4,10,1]=>[10,3,2,9,6,5,8,7,4,1]=>[1,2,1,2,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,8,7,9,6,10,1]=>[10,5,4,3,2,9,8,7,6,1]=>[1,1,2,1,1,2,1,1]
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,8,7,9,6,10,1]=>[10,3,2,5,4,9,8,7,6,1]=>[1,2,2,1,2,1,1]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,10,1]=>[10,7,6,5,4,3,2,9,8,1]=>[1,1,1,2,1,1,2,1]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,10,1]=>[10,7,4,3,6,5,2,9,8,1]=>[1,1,2,2,1,2,1]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,10,1]=>[10,3,2,7,6,5,4,9,8,1]=>[1,2,1,2,1,2,1]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,10,1]=>[10,5,4,3,2,7,6,9,8,1]=>[1,1,2,1,2,2,1]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,10,1]=>[10,3,2,5,4,7,6,9,8,1]=>[1,2,2,2,2,1]
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,7,6,8,5,9,4,10,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,1,1,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,9,4,10,3]=>[2,1,10,9,6,5,8,7,4,3]=>[2,1,1,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,8,7,9,6,10,3]=>[2,1,10,5,4,9,8,7,6,3]=>[2,1,2,1,2,1,1]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,10,3]=>[2,1,10,7,6,5,4,9,8,3]=>[2,1,1,2,1,2,1]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,10,3]=>[2,1,10,5,4,7,6,9,8,3]=>[2,1,2,2,2,1]
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,2,1,10,9,8,7,6,5]=>[1,2,1,1,1,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,10,5]=>[4,3,2,1,10,7,6,9,8,5]=>[1,2,1,1,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,8,7,9,6,10,5]=>[2,1,4,3,10,9,8,7,6,5]=>[2,2,1,1,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,10,5]=>[2,1,4,3,10,7,6,9,8,5]=>[2,2,1,2,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,9,8,10,7]=>[6,5,4,3,2,1,10,9,8,7]=>[1,1,2,1,1,1,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,9,8,10,7]=>[6,3,2,5,4,1,10,9,8,7]=>[1,2,2,1,1,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,9,8,10,7]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,2,1,1,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,9,8,10,7]=>[4,3,2,1,6,5,10,9,8,7]=>[1,2,1,2,1,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,9,8,10,7]=>[2,1,4,3,6,5,10,9,8,7]=>[2,2,2,1,2,1]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,2,1,1,1,2]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9]=>[8,7,4,3,6,5,2,1,10,9]=>[1,1,2,2,1,1,2]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9]=>[8,3,2,7,6,5,4,1,10,9]=>[1,2,1,2,1,1,2]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9]=>[8,5,4,3,2,7,6,1,10,9]=>[1,1,2,1,2,1,2]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9]=>[8,3,2,5,4,7,6,1,10,9]=>[1,2,2,2,1,2]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,1,2,1,1,2]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9]=>[2,1,8,5,4,7,6,3,10,9]=>[2,1,2,2,1,2]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[1,2,1,1,2,1,2]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,2,1,2,1,2]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[1,1,2,1,1,2,2]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]=>[1,2,2,1,2,2]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,2,1,2,2]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[1,2,1,2,2,2]
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,2,1,1,1,1,1]
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[1,1,1,1,2,2,1,1,1,1]
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[1,1,1,2,1,2,1,1,1,1]
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>[1,1,1,1,2,1,2,1,1,1]
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>[1,1,1,2,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[1,1,2,1,1,2,1,1,1,1]
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>[1,1,2,1,2,2,1,1,1]
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[1,1,1,2,1,1,2,1,1,1]
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>[1,1,2,2,1,2,1,1,1]
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>[1,1,1,1,2,1,1,2,1,1]
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>[1,1,1,2,2,1,2,1,1]
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>[1,1,2,1,2,1,2,1,1]
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>[1,1,1,2,1,2,2,1,1]
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>[1,1,2,2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[1,2,1,1,1,2,1,1,1,1]
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>[1,2,1,1,2,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>[1,2,1,2,1,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>[1,2,1,1,2,1,2,1,1]
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>[1,2,1,2,2,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>[1,1,2,1,1,1,2,1,1,1]
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>[1,1,2,1,1,2,2,1,1]
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>[1,2,2,1,1,2,1,1,1]
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>[1,2,2,1,2,2,1,1]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>[1,1,1,2,1,1,1,2,1,1]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>[1,1,2,2,1,1,2,1,1]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>[1,2,1,2,1,1,2,1,1]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>[1,1,2,1,2,1,2,1,1]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>[1,2,2,2,1,2,1,1]
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>[1,1,1,1,2,1,1,1,2,1]
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>[1,1,1,2,2,1,1,2,1]
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>[1,1,2,1,2,1,1,2,1]
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>[1,1,1,2,1,2,1,2,1]
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>[1,1,2,2,2,1,2,1]
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>[1,2,1,1,2,1,1,2,1]
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>[1,2,1,2,2,1,2,1]
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>[1,1,2,1,1,2,1,2,1]
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>[1,2,2,1,2,1,2,1]
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>[1,1,1,2,1,1,2,2,1]
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>[1,1,2,2,1,2,2,1]
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>[1,2,1,2,1,2,2,1]
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>[1,1,2,1,2,2,2,1]
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[1,2,2,2,2,2,1]
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,1,1,1,2,1,1,1,1]
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>[2,1,1,1,2,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>[2,1,1,2,1,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>[2,1,1,1,2,1,2,1,1]
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>[2,1,1,2,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>[2,1,2,1,1,2,1,1,1]
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>[2,1,2,1,2,2,1,1]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>[2,1,1,2,1,1,2,1,1]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>[2,1,2,2,1,2,1,1]
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>[2,1,1,1,2,1,1,2,1]
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>[2,1,1,2,2,1,2,1]
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>[2,1,2,1,2,1,2,1]
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>[2,1,1,2,1,2,2,1]
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>[2,1,2,2,2,2,1]
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[1,2,1,1,1,1,2,1,1,1]
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>[1,2,1,1,1,2,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>[1,2,1,1,2,1,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>[1,2,1,1,1,2,1,2,1]
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>[1,2,1,1,2,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,2,1,1,1,2,1,1,1]
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>[2,2,1,1,2,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>[2,2,1,2,1,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>[2,2,1,1,2,1,2,1]
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>[2,2,1,2,2,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,1,2,1,1,1,1,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>[1,1,2,1,1,1,2,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>[1,2,2,1,1,1,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>[1,2,2,1,1,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,2,1,1,1,2,1,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>[2,1,2,1,1,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[1,2,1,2,1,1,2,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>[1,2,1,2,1,2,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,2,2,1,1,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>[2,2,2,1,2,2,1]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[1,1,1,2,1,1,1,1,2,1]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>[1,1,2,2,1,1,1,2,1]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>[1,2,1,2,1,1,1,2,1]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>[1,1,2,1,2,1,1,2,1]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>[1,2,2,2,1,1,2,1]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,1,2,1,1,1,2,1]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>[2,1,2,2,1,1,2,1]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[1,2,1,1,2,1,1,2,1]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,2,1,2,1,1,2,1]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[1,1,2,1,1,2,1,2,1]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>[1,2,2,1,2,1,2,1]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,2,1,2,1,2,1]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[1,2,1,2,2,1,2,1]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,2,2,2,1,2,1]
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,1,1,1,2,1,1,1,1,2]
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>[1,1,1,2,2,1,1,1,2]
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>[1,1,2,1,2,1,1,1,2]
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>[1,1,1,2,1,2,1,1,2]
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>[1,1,2,2,2,1,1,2]
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>[1,2,1,1,2,1,1,1,2]
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>[1,2,1,2,2,1,1,2]
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>[1,1,2,1,1,2,1,1,2]
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>[1,2,2,1,2,1,1,2]
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>[1,1,1,2,1,1,2,1,2]
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>[1,1,2,2,1,2,1,2]
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>[1,2,1,2,1,2,1,2]
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>[1,1,2,1,2,2,1,2]
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>[1,2,2,2,2,1,2]
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,1,1,2,1,1,1,2]
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>[2,1,1,2,2,1,1,2]
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>[2,1,2,1,2,1,1,2]
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>[2,1,1,2,1,2,1,2]
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>[2,1,2,2,2,1,2]
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[1,2,1,1,1,2,1,1,2]
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>[1,2,1,1,2,2,1,2]
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,2,1,1,2,1,1,2]
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>[2,2,1,2,2,1,2]
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[1,1,2,1,1,1,2,1,2]
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>[1,2,2,1,1,2,1,2]
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,2,1,1,2,1,2]
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[1,2,1,2,1,2,1,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,2,2,1,2,1,2]
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[1,1,1,2,1,1,1,2,2]
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>[1,1,2,2,1,1,2,2]
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>[1,2,1,2,1,1,2,2]
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>[1,1,2,1,2,1,2,2]
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>[1,2,2,2,1,2,2]
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,1,2,1,1,2,2]
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>[2,1,2,2,1,2,2]
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[1,2,1,1,2,1,2,2]
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,2,1,2,1,2,2]
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[1,1,2,1,1,2,2,2]
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>[1,2,2,1,2,2,2]
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,2,1,2,2,2]
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[1,2,1,2,2,2,2]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,3,4,5,6,7,8]=>[2,7]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>[7,2]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[9]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[9]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[10]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,2,1,3,4,5,6,7,8]=>[2,7]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[11]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[2,7]
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[2,8]
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[1,2,1,5]
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[9,2,3,1,4,5,6,7,8]=>[3,6]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
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